Firstly, if you come to a session called "The architecture of affordability", you might be forgiven for thinking that it will be about that: the architecture. But what I walked away with - reaffirmed from a previous tour of affordable housing projects here in the US in 2006 - is that the architecture they're really referring to is a financial one. It's about the maths.

And although the US has a very different framework for encouraging and subsidising affordable housing, there are some transferable ideas to take away. But no silver bullet. Just in case you were hoping. (In Australia, where the land is say 60% of the cost of the ultimate house and land combination versus here where it may be as little as 30%, there are very different economic fndamentals at play - and that's before youi consider tax, and housing authorities and the like.)

Hana Eskra of Gorman USA, a 28 year old company working with civic leaders to solve community problems and primarily using the lever of tax credits to fund them, spoke a lot about the maths.

First, she wanted us to be clear just what affordable housing is, and I was surprised to find that this definition was actually established as far back as 1937, in the Housing Act of that year. It said that affordable housing is that which costs not more than 30% of your income. In that context, low income is 80% of median family income (median is about $51k pa) and this leads us to the "maths problem", Eskra says: they can't pay enough for a building we'd build. What they could pay is $520 a month - and that "barely allows us to keep the lights on".

"There's no money left to build that building and that's the maths problem," she says. "On one hand it costs about $200-$250k to build a unit. On the other, even if they earn $20/hr they can still only afford an $85k mortgage."

Dealing with that maths problem takes a sophisticated layering of financial instruments (which, ironically, means that accountants and lawyers get rich while others get affordable housing) and also the Choice Neighbourhoods Program which took over from a prior program (HUD 6). It's designed to not only have people develop a building but also the neighbourhood. With a possible planning grant of $300k and an implementation grant of $20-30million, the program wants to make sure that "instead of just focusing on public housing, you need to have a plan for transforming neighbourhoods.

Example: Nehemiah Spring Creek

Across the country at Nehemiah Spring Creek, in Brooklyn, New York, Alexander Gorlin Architects and others are dealing with the maths problem too. On a 50 acre site at the edge of the Jamaica Bay, which was landfill for 50 years with pockets of methane gas (which meant that when developed the whole site needed to be capped with four metres of sand) a group of people inspired by Johnny Ray Youngblood are creating something quite different to the identical, defensive, front loaded homes with big fences - "the suburban transferred to the urban" - that are nearby.

"At first I thought we should have ten different architects involved," says Gorlin, "but we couldn't afford it." Instead they created a series of three-bedroom units, 20x40 feet, sold as individual homes, and inspired by Bruno Taut's housing in Berlin, which used different colours chosen to reflect the direction facing the sun, to add variety. (Here, 12 colours somehow related religiously in some arcane way that I missed were used to achieve a similar effect.)

To achieve construction efficiency, the homes were brought forward to the street, incorporated rear parking, and were built using pre-fab modules built in a Brooklyn navy yard, with facades installed on site. They're 20 feet wide, because that's the maximum that can be transported through the streets of New York. (NY codes limit modules to 18 feet on bridges which is why the developers had to tender out to prefab firms in the city and not beyond.) Selling for $100/sq foot, there are now 568 townhouses, 700 units. a school on the site, and a large shopping mall nearby.

Example: Newburgh and Habitat for Humanity

Newburgh, NY, is one one hand an historic centre of American architecture. On the other, it includes a low income population that needs affordable housing. In a joint Leyland Alliance and Habitat for Humanity project, aimed at the existing population and designed for 25% to 60% of area median income (median income is $36000 here) some of the areas 'missing teeth' have been rebuilt and restored.

Habitat for Humanity operates on a model that requires a $1500 downpayment, a commitment (and proof of ability) to pay the mortgage, 400 hours of community service (building the homes), and participation in financial classes for 6 months.

The project had to overturn 86 planning variations just to put back what they'd just demolished but then went on to deliver affordable and contextually sympathetic architecture for $79 a square foot - versus the typical Habitat for Humanity building costs (for far less attractive homes) of $119 sq/ft. Part of this was achieved through good design and a production friendly approach: precast foundation systems were put in in a day, truss framing was done in three days, facades used pre-painted Hardie product.

Energy operating costs now average $80/mth, and, if educational achievements are any indication, the result is not just about money : grade point averages went from Ds to Bs and As.

The key, Leyland's Giovanni Palladino says, is to develop trust in the community, and Habitat was key in achieving that. "It's essential to find the leaders in the existing community to help you."

But, he acknowledge, in a place where 45% of the population is African-American it's disappointing that none of those people have applied.